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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Determinants

NDA 2019 · Mathematics · Determinants

If A is a square matrix of order n > 1 , then which one of the...

If AA is a square matrix of order n>1n > 1, then which one of the following is correct?

Options

  1. Adet⁡⁡(−A)=det⁡⁡A\operatorname\det(-\mathrm{A})=\operatorname\det \mathrm{A}
  2. Bdet⁡⁡(−A)=(−1)ndet⁡⁡A\operatorname\det(-\mathrm{A})=(-1)^{\mathrm{n}} \operatorname\det \mathrm{A}
  3. Cdet⁡⁡(−A)=−det⁡⁡A\operatorname\det(-\mathrm{A})=-\operatorname\det \mathrm{A}
  4. Ddet⁡⁡(−A)=ndet⁡⁡A\operatorname\det(-\mathrm{A})=\mathrm{n} \operatorname\det \mathrm{A}

Correct answer

B. det⁡⁡(−A)=(−1)ndet⁡⁡A\operatorname\det(-\mathrm{A})=(-1)^{\mathrm{n}} \operatorname\det \mathrm{A}

Step-by-step solution

A is square matrix of order n>1\mathrm{n} > 1. det⁡⁡(−A)=(−1)ndet⁡⁡A\operatorname\det(-\mathrm{A})=(-1)^{\mathrm{n}} \operatorname\det \mathrm{A}
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